Unifying transcranial focused ultrasound and transcranial magnetic stimulation effects with calcium-dependent synaptic plasticity theory

Low-intensity transcranial focused ultrasound stimulation (TUS) is an emerging technology that shares features of both established invasive neurostimulation techniques such as deep brain stimulation (DBS) and noninvasive techniques such as transcranial magnetic stimulation (TMS). Like DBS, TUS can target non-superficial brain structures with millimeter-level precision. Like TMS, but unlike DBS, the most important physiological effect of TUS from a clinical perspective is its ability to induce lasting neuroplastic changes (long term potentiation/depression; LTP/LTD) from relatively short stimulation sessions. Thus follows the intriguing possibility that, although TUS and TMS have fundamentally different primary mechanisms of action -- acoustic versus electromagnetic -- they might nevertheless share a common secondary mechanism of plasticity induction through temporally patterned stimulation. A quantitative mathematical theory of this secondary mechanistic pathway could therefore have important explanatory and predictive value in both modalities. Two major challenges to the development of such a theory, however, are: i) experimental results showing contradictory plasticity effects between TUS and TMS for nominally similar stimulation parameters, and ii) the markedly different temporal structures of their stimulation waveforms (ranging from discrete pulses in TMS to continuous sinusoidal oscillations in TUS), even for highly aligned protocol designs such as continuous theta burst (cTB) stimulation. Here we show that a mathematical model of calcium-dependent synaptic plasticity in corticothalamic circuits, already developed extensively for TMS, can indeed provide such a unified description of stimulation effects across these two modalities. Numerical simulations using this model for a range of TUS and TMS protocols reproduced plasticity effects consistent with experimentally observed changes in cortical excitability. In particular, our model addresses both of the above challenges, by i) reconciling apparently contradictory results across modalities for the same stimulation parameters, and ii) introducing a simple algebraic approach, which we term the 'equivalent energy principle', for relating corresponding TMS and TUS waveforms. The ability of the model to account for differing effects across multiple stimulation modalities provides further support for the underlying general theory describing calcium-based regulation of stimulation plasticity effects, which spans multiple scales of system organization -- from ion channel kinetics to neural population activity. Our work also provides a foundation for future bidirectional exchange of new experimental observations and insights between experimental and theoretical TUS and TMS research, including strategies for model-based protocol optimization and discovery of novel plasticity-inducing TUS and TMS paradigms.